Generation of Quasi-Electrostatic Slow Extraordinary Waves by Kappa Distribution with a Loss Cone

A detailed study of the generation of slow extraordinary (SE) waves in the Earth’s magnetosphere has been carried out. Assuming that energetic electrons are distributed in accordance with the \(\kappa \)-function with a loss cone, the instability growth rate of SE waves is calculated and its dependence on both the parameters of the hot particle distribution function and the cold particle density, characterized by the ratio of the electron plasma frequency to the electron cyclotron frequency, \({{\omega }_{p}}{\text{/}}{{\omega }_{c}}\), is studied. This ratio is one of the key parameters of the problem. For various \({{\omega }_{p}}{\text{/}}{{\omega }_{c}}\) values, the dependences of the instability growth rate on the parameter \(\kappa \) of the distribution function, the loss cone parameter \(l\), and the temperature of the distribution and its anisotropy are obtained. A nonmonotonic, quasi-periodic dependence of the growth rate on the ratio of the frequency to the electron gyrofrequency, which manifests itself in the dependence of the equatorial growth rate on the \(L\)-shell or the dependence of the growth rate on the latitude on a fixed \(L\)-shell, is revealed and explained.